allowing a well-defined class of pseudo-differential operators in the complete range \(0\le \delta <\rho \le 1.\)  The classes in (REF ) become effective in handling certain classes of operators, for example resolvent operators
for vector fields on a compact Lie group \(G\)  which belong to the class \( \Psi ^0_{0,0}(G\times \widehat{G})\)  or in parametrices of Hörmander sub-Laplacians that have symbols in the class \( \Psi ^{-1}_{\frac{1}{2},0}(G\times \widehat{G}).\) 
See [1]} for this and for other examples of the appearance of different symbol classes as
parametrices for hypoelliptic operators which cannot be handled by the standard theory
in view of the restriction in (REF ).
